| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 36125.4-a1 |
36125.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{6} \cdot 17^{2} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.046218757$ |
$3.770763696$ |
2.091360133 |
\( \frac{188416}{125} a - \frac{12288}{125} \) |
\( \bigl[0\) , \( i\) , \( i\) , \( 2 i + 2\) , \( i - 3\bigr] \) |
${y}^2+i{y}={x}^{3}+i{x}^{2}+\left(2i+2\right){x}+i-3$ |
| 36125.4-b1 |
36125.4-b |
$2$ |
$17$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{10} \cdot 17^{4} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$17$ |
17B |
$1$ |
\( 2 \) |
$0.736722346$ |
$1.090771932$ |
3.214384227 |
\( \frac{434176}{5} a - \frac{73728}{5} \) |
\( \bigl[0\) , \( i - 1\) , \( i\) , \( 79 i + 41\) , \( 14 i + 286\bigr] \) |
${y}^2+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(79i+41\right){x}+14i+286$ |
| 36125.4-b2 |
36125.4-b |
$2$ |
$17$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{26} \cdot 17^{8} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$17$ |
17B |
$1$ |
\( 2 \) |
$12.52427988$ |
$0.064163054$ |
3.214384227 |
\( \frac{267336867946496}{762939453125} a + \frac{71438985142272}{762939453125} \) |
\( \bigl[0\) , \( i - 1\) , \( i\) , \( 5439 i + 4311\) , \( -266410 i - 400132\bigr] \) |
${y}^2+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(5439i+4311\right){x}-266410i-400132$ |
| 36125.4-c1 |
36125.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{9} \cdot 17^{8} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$2.380973278$ |
$0.630170152$ |
3.000836587 |
\( -\frac{512}{5} a + \frac{1216}{5} \) |
\( \bigl[i + 1\) , \( 0\) , \( 1\) , \( 55 i - 35\) , \( 128 i + 454\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(55i-35\right){x}+128i+454$ |
| 36125.4-c2 |
36125.4-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{11} \cdot 17^{8} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$7.142919834$ |
$0.210056717$ |
3.000836587 |
\( -\frac{1147637248}{125} a + \frac{3969820864}{125} \) |
\( \bigl[i + 1\) , \( 0\) , \( 1\) , \( 1320 i - 5430\) , \( -57218 i + 150357\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(1320i-5430\right){x}-57218i+150357$ |
| 36125.4-d1 |
36125.4-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{9} \cdot 17^{2} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.204163828$ |
$2.598258101$ |
3.182821922 |
\( -\frac{512}{5} a + \frac{1216}{5} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( -4 i\) , \( -5 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}-4i{x}-5i-4$ |
| 36125.4-d2 |
36125.4-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{11} \cdot 17^{2} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.612491484$ |
$0.866086033$ |
3.182821922 |
\( -\frac{1147637248}{125} a + \frac{3969820864}{125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( -219 i + 245\) , \( -1023 i - 2155\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-219i+245\right){x}-1023i-2155$ |
| 36125.4-e1 |
36125.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{7} \cdot 17^{7} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.225276466$ |
$0.966306192$ |
3.482976715 |
\( -\frac{31292928}{10625} a + \frac{54407104}{10625} \) |
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( 64 i + 19\) , \( -52 i - 167\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(64i+19\right){x}-52i-167$ |
| 36125.4-e2 |
36125.4-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{5} \cdot 17^{8} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.450552933$ |
$0.966306192$ |
3.482976715 |
\( \frac{41426432}{7225} a + \frac{61119424}{7225} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i\) , \( -75 i - 3\) , \( -194 i + 202\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-75i-3\right){x}-194i+202$ |
| 36125.4-f1 |
36125.4-f |
$2$ |
$17$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{10} \cdot 17^{10} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$17$ |
17B |
$1$ |
\( 2 \) |
$2.971758242$ |
$0.264551052$ |
3.144727081 |
\( \frac{434176}{5} a - \frac{73728}{5} \) |
\( \bigl[0\) , \( -i\) , \( i\) , \( -1523 i + 22\) , \( 15679 i - 17219\bigr] \) |
${y}^2+i{y}={x}^{3}-i{x}^{2}+\left(-1523i+22\right){x}+15679i-17219$ |
| 36125.4-f2 |
36125.4-f |
$2$ |
$17$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{26} \cdot 17^{2} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$17$ |
17B |
$1$ |
\( 2 \cdot 17 \) |
$0.174809308$ |
$0.264551052$ |
3.144727081 |
\( \frac{267336867946496}{762939453125} a + \frac{71438985142272}{762939453125} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -163 i - 374\) , \( -6800 i - 1106\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-163i-374\right){x}-6800i-1106$ |
| 36125.4-g1 |
36125.4-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{6} \cdot 17^{7} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.177399634$ |
2.354799268 |
\( \frac{1531324}{2125} a + \frac{157343}{2125} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( 25 i\) , \( 84 i + 19\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+25i{x}+84i+19$ |
| 36125.4-g2 |
36125.4-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{9} \cdot 17^{8} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.588699817$ |
2.354799268 |
\( -\frac{18924185611}{4515625} a + \frac{9269513798}{4515625} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( -130 i - 110\) , \( 730 i + 291\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-130i-110\right){x}+730i+291$ |
| 36125.4-h1 |
36125.4-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
36125.4 |
\( 5^{3} \cdot 17^{2} \) |
\( 5^{6} \cdot 17^{8} \) |
$2.46389$ |
$(-a-2), (2a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.626634923$ |
$0.914544529$ |
6.877026502 |
\( \frac{188416}{125} a - \frac{12288}{125} \) |
\( \bigl[0\) , \( -i - 1\) , \( 1\) , \( -48 i - 19\) , \( 169 i - 118\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-48i-19\right){x}+169i-118$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
